CN107015945A - A kind of high-order interacting multiple model filters method based on mixture transition distribution - Google Patents
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Abstract
A kind of high-order interacting multiple model filters method based on mixture transition distribution, the present invention relates to the high-order interacting multiple model filters method based on mixture transition distribution.The problem of present invention is in order to solve many markovian arrange parameters of high-order in existing method, cumbersome setting up procedure and relatively low precision.The present invention includes：One：N rank Model sequence transition probabilities are obtained using mixture transition distribution model；Two：The k moment is handled in real time；Three：State during to k=1 is initialized；Four：State during to k=2 is initialized；Five：K is judged, as k=n, then to the n rank Model sequence probability at k moment, n rank Model sequence state estimations and corresponding covariance are initialized；Six：State during to 3≤k≤n interacts formula multiple model filtering algorithm；Seven：To k>State during n carries out General High-order interacting multiple model filters.The present invention is used for maneuvering target tracking field.
Description
Technical Field
The invention relates to a high-order interactive multi-model filtering method based on mixed transfer distribution.
Background
In the problem of model uncertainty of target tracking, a multi-model filtering algorithm is often adopted for solving. Classical algorithmic interactive multi-model filtering algorithms (IMM) are proposed, among others, in H.A.P.Blom, Y.Bar-Shalom. "The interactive multi-model algorithm for systems with Markovian switching coeffients," IEEE Transactions on AutomaticControl, vol.33(8), pp.780-783,1988. Although the algorithm can adaptively identify the model at the current moment, the accuracy is not very high.
A generalized High-order interactive multi-model filtering method (IMMn) is proposed in P.Suchomski, "High-order interacting multiple-model estimation for hybrid systems with Markovian switching parameters," International Journal of systems Science, vol.32(5), pp.669-679,2001, and a target state is estimated more accurately by using a High-order model sequence. However, this method has a disadvantage in that the setting of the high-order markov chain is complicated. The number of the parameters increases exponentially along with the increase of the order, and one time, the number of the parameters required to be set is too many and is more complicated; it is difficult to set all parameters reasonably without affecting the overall state estimation, and therefore, the algorithm is influenced to be applied to higher orders. Therefore, a simpler method is needed to replace the high-order markov chain and apply to the high-order interactive multi-model filtering method.
Bisoxin; fipronil; a great plant; high cleanliness; field star; zhao Vietnam; zhao Qian; a bushy Japanese steel; a trypan; plum blossom imagination; clearing stone; flood control; "an interactive multi-model tracking method based on adaptive transition probability matrix", china, 2015-09-02 and korean red; plum yang; aging for megaly; cooling; weft is intelligently built; in the two patents, canopie, China, 2009-07-08, which are the interactive multi-model filtering methods based on fuzzy inference, are improved, but the orders of the methods are still in the first order, prior information of a high-order model sequence is not fully utilized, and the estimation accuracy is to be further improved.
Disclosure of Invention
The invention aims to solve the problems of more setting parameters, complicated setting process and lower precision of a high-order Markov chain in the conventional generalized high-order interactive multi-model filtering method, and provides a high-order interactive multi-model filtering method based on mixed transfer distribution.
A high-order interactive multi-model filtering method based on mixed transfer distribution is realized according to the following steps:
the method comprises the following steps: obtaining n-order model sequence transition probability rho (m) by adopting a mixed transition distribution modelk|mk-n,...,mk-1)；
Step two: the estimated state vector isAnd relativeThe corresponding covariance isProcessing the k moment in real time; when k is equal to 1, turning to step three; when k is 2, turning to step four; when k is more than or equal to 3 and less than or equal to n, turning to the sixth step; when k is>When n, turning to the seventh step;
step three: initializing the state when k is equal to 1, turning to step two, and waiting to process radar observation data at the next time when k is equal to k + 1;
step four: initializing the state when k is 2, and then turning to the fifth step;
step five: judging k, and when k is equal to n, determining the n-order model sequence probability U at the moment kk(mk-n+1,...,mk) N-order model sequence state estimationAnd withCorresponding covarianceAfter initialization, waiting for processing radar observation data at the next moment when k is equal to k +1 in the second step; when k is not equal to n, directly executing step two to process radar observation data at the moment when k is equal to k + 1;
step six: after interactive multi-model filtering is carried out on the state when k is more than or equal to 3 and less than or equal to n, the step five is carried out;
step seven: and after the generalized high-order interactive multi-model filtering is carried out on the state when k is larger than n, the step II is carried out to wait for processing the radar observation data at the next k-k +1 moment.
The invention has the beneficial effects that:
the method utilizes the received radar observation data to perform real-time processing, thereby realizing effective tracking of the maneuvering target. The higher the order, the smaller the error in the model-invariant region, and the higher the estimation accuracy of the target state. Compared with IMM, the precision is high, the estimation performance is better, and the improvement is about 10%; compared with IMMn, the method solves the problem that the high-order Markov chain is difficult to set, and reduces the possibility of reducing the filtering effect due to unsatisfactory parameter setting.
The invention provides a high-order interactive multi-model filtering method based on mixed transfer distribution. The mixed transfer distribution model has the advantages of less required parameters and simple setting, is used for replacing a high-order Markov chain to approach a high-order model sequence transfer probability matrix, and is applied to a high-order interactive multi-model filtering method, so that a high-order algorithm can be flexibly used.
Drawings
FIG. 1 is a comparison graph of the position root mean square error of the method of the present invention and an interactive multi-model algorithm of order 2;
FIG. 2 is a graph comparing the RMS error of the speed of the method of the present invention with that of an interactive multi-model algorithm of order 2;
FIG. 3 is a comparison of the root mean square error of the positions of the method of the present invention for different orders;
FIG. 4 is a comparison graph of the root mean square error of the velocity of the method of the present invention in different orders.
Detailed Description
The first embodiment is as follows: a high-order interactive multi-model filtering method based on mixed transfer distribution comprises the following steps:
the method comprises the following steps: obtaining n-order model sequence transition probability rho (m) by adopting a mixed transition distribution modelk|mk-n,...,mk-1)；
Step two: the estimated state vector isAnd a corresponding covariance ofProcessing the k moment in real time; when k is equal to 1, turning to step three; when k is 2, turning to step four; when k is more than or equal to 3 and less than or equal to n, turning to the sixth step; when k is>When n, turning to the seventh step;
step three: initializing the state when k is equal to 1, turning to step two, and waiting to process radar observation data at the next time when k is equal to k + 1;
step four: initializing the state when k is 2, and then turning to the fifth step;
step five: judging k, and when k is equal to n, determining the n-order model sequence probability U at the moment kk(mk-n+1,...,mk) N-order model sequence state estimationAnd withCorresponding covarianceAfter initialization, waiting for processing radar observation data at the next moment when k is equal to k +1 in the second step; when k is not equal to n, directly executing step two to process radar observation data at the moment when k is equal to k + 1;
step six: after interactive multi-model filtering is carried out on the state when k is more than or equal to 3 and less than or equal to n, the step five is carried out;
step seven: and after the generalized high-order interactive multi-model filtering is carried out on the state when k is larger than n, the step II is carried out to wait for processing the radar observation data at the next k-k +1 moment.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: in the first step, a mixed transition distribution model is adopted to obtain an n-order model sequence transition probability rho (m)k|mk-n,...,mk-1) The specific process comprises the following steps:
wherein m isjM is the model at time j, j is k-n, …, k, and the number of models is rjThe value range of (1) to r;is from the model mk-gTransfer to model mkThe probability of (a) of (b) being,is an element in a first order Markov chain, λgIs each step size coefficient, satisfying the following conditions:
other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: the model specifically comprises:
Xk+1＝Fk(mk)Xk+Gk(mk)uk(mk)+k(mk)vk(mk)
wherein XkIs determined by x-axis position x at time kkSpeed of x axisy-axis position ykSpeed of y axisThe constituent state vectors. Fk(mk) Representing the model m at time kkSystem transfer matrix ofk(mk) Is an input control matrix, uk(mk) Is the input of a signal, and the signal is,k(mk) Is a matrix of noise coefficients, vk(mk) Is the k time model mkZero mean white Gaussian process noise with covariance of Qk(mk)。
Where T denotes the sampling interval.
(1) When the model is a uniform motion model
(2) When the model cooperates with the turning model
(3) When the model is in uniform accelerated motion
Wherein, ax，ayThe acceleration is respectively in the directions of an x axis and a y axis, the x axis is in the horizontal direction, the y axis is in the vertical direction, and the x axis is perpendicular to the y axis.
The three models listed above are the most commonly used models in maneuvering target tracking, but are merely exemplary, and other models may be used in practical applications according to requirements.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment mode and one of the first to third embodiment modes is: the specific process of initializing the state when k is 1 in the third step is
Wherein z isk＝[xkyk]TIndicating the received radar observation data at time k, zk(j) Denotes zkThe jth value of (a). r isijIs the ith row and jth column element of the observed noise covariance R, i.e.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is: the specific process of initializing the state when k is 2 in the fourth step is
Then initialize the k-time model probabilityState estimation of modelsCorresponding covariance
Other steps and parameters are the same as in one of the first to fourth embodiments.
The sixth specific implementation mode: the difference between this embodiment and one of the first to fifth embodiments is: in the fifth step, k is judged, and when k is equal to n, the n-order model sequence probability U at the moment k is judgedk(mk-n+1,...,mk) N-order model sequence state estimationAnd withCorresponding covarianceThe specific process of initializing is as follows:
other steps and parameters are the same as those in one of the first to fifth embodiments.
The seventh embodiment: the difference between this embodiment and one of the first to sixth embodiments is: the specific process of carrying out interactive multi-model filtering on the state when k is more than or equal to 3 and less than or equal to n in the sixth step is as follows:
calculating the probability of mixture
Where ρ (m)k|mk-1) Is a first-order model transition probability, and 0C can be preset according to actual requirements1(mk) Is the normalization constant:
computing hybrid state estimates
Computing covariance corresponding to hybrid state estimates
HandleAndas input, Kalman filtering is performed to obtain state estimates of the models at time kCorresponding covarianceAnd likelihood function Λk(mk)。
Calculating k moment model probability
Calculating the state at time k
ComputingCorresponding covariance
Other steps and parameters are the same as those in one of the first to sixth embodiments.
The specific implementation mode is eight: the present embodiment differs from one of the first to seventh embodiments in that: the specific process of carrying out generalized high-order interactive multi-model filtering on the state when k is greater than n in the step seven is as follows:
calculating the probability of mixture
Wherein, Cn(mk-n+1,...,mk) Is a normalization constant;
computing a hybrid state estimate for an n-th order model sequence
ComputingCorresponding covariance
HandleAndas input, Kalman filtering is carried out to obtain state estimation of each model sequence at the k momentCorresponding covarianceAnd likelihood function Λk(mk-n+1,...,mk)。
Calculating n-order model sequence probability at k moment
Calculating model probability at time k
Calculating the state at time k
ComputingCorresponding covariance
Other steps and parameters are the same as those in one of the first to seventh embodiments.
The specific implementation method nine: the present embodiment differs from the first to eighth embodiments in that: kalman filtering used in the above steps is to estimate the state by inputting the k-1 timeAnd the corresponding covarianceObtain the state at time kCorresponding covarianceAnd likelihood function ΛkThe method comprises the following specific steps:
and (3) state prediction:
and (3) covariance prediction:
and (3) calculating an observation predicted value:
wherein HkIs an observation matrix;
and (3) calculating innovation:
calculating innovation covariance:
r is the observed noise covariance,is HkTransposing;
and (3) calculating a likelihood function:
Λk＝N(zk；vk|k-1,Sk|k-1)
wherein N (z)k；vk|k-1,Sk|k-1) Denotes zkObey a mean value vk|k-1Covariance of Sk|k-1(ii) a gaussian distribution of;
and (3) calculating gain:
whereinIs Sk|k-1The inverse of (1);
calculating the state:
and (3) calculating covariance:
other steps and parameters are the same as those in one to eight of the embodiments.
The first embodiment is as follows:
using a kalman linear filter model, the observation equation is:
zk+1＝Hk+1Xk+1+wk+1
wk+1is white gaussian observation noise with zero mean, whose covariance is R, and is uncorrelated with process noise. Hk+1Is the observation matrix at time k + 1.
zk+1＝[xk+1,yk+1]T
In the simulation scene, two models of constant-speed linear motion and coordinate turning motion are used together. The specific simulation scenario is as follows: the maneuvering target is first X1＝[1000,50,1000,50]TThe initial state of the flying robot flies for 40s in uniform motion, then turns at w-3 rad/s for 40-80s, and finally continues to move at uniform motion for 40 s. Wherein,R＝1Im2. The sampling interval T is 1 s.
The high-order interactive multi-model filtering method based on mixed transfer distribution (the order n is 2) comprises the following steps:
the method comprises the following steps: and obtaining the 2-order model sequence transition probability rho (l | i, j) by adopting a mixed transition distribution model.
ρ(l|i,j)＝λ1pjl+λ2pil,i,j,l∈{1,2}
Wherein λ is1＝0.67,λ2＝0.23，piji, j ∈ {1,2} is an element in the first order model transition probability Π,
step two: the estimated state vector isAnd a corresponding covariance ofThe real-time processing is carried out on the k time under the following four conditions.
(1) When k is equal to 1, turning to step three;
(2) when k is 2, turning to step four;
(3) when k is more than or equal to 3 and less than or equal to n, turning to the sixth step;
(4) when k is larger than n, turning to the seventh step;
step three: initializing the state when k is 1
Turning to step two to wait for processing radar observation data at the next moment when k is equal to k + 1;
step four: initializing the state when k is 2
Then initialize the k-time model probabilityState estimation of modelsCorresponding covariance
Then turning to the fifth step;
step five: judging k, when k is n, then judging Uk(mk-1,mk)，And withCorresponding toInitialization is performed.
Turning to step two to wait for processing radar observation data at the next moment when k is equal to k + 1;
step six: and carrying out interactive multi-model filtering when k is more than or equal to 3 and less than or equal to n. The specific steps are as follows:
calculating the mixing probability:
wherein C is1(mk) Is a normalization constant;
calculating a hybrid state estimate:
computingThe corresponding covariance:
handleAndas input, Kalman filtering is performed to obtain state estimates of the models at time kCorresponding covarianceAnd likelihood function Λk(mk)。
Calculating the probability of the model at the moment k:
calculating the state at time k:
computingThe corresponding covariance:
turning to the fifth step;
step seven: and carrying out generalized high-order interactive multi-model filtering when k is greater than n. The specific steps are as follows:
calculating the mixing probability:
wherein, C2(mk-1,mk) Is the normalization constant:
calculating a mixture state estimate of the 2 nd order model sequence:
computingThe covariance of (a):
handleAndas input, Kalman filtering is carried out to obtain state estimation of each model sequence at the k momentCorresponding covarianceAnd likelihood function Λk(mk-1,mk)。
Calculating the probability of the 2 nd order model sequence at the k moment:
calculating the model probability at the k moment:
calculating the state at time k:
computingThe corresponding covariance:
turning to step two to wait for processing radar observation data at the next moment when k is equal to k + 1;
wherein, the Kalman filtering step is to estimate the state by inputting the k-1 momentAnd the corresponding covarianceObtain the state at time kCorresponding covarianceAnd likelihood function ΛkThe method comprises the following specific steps:
and (3) state prediction:
and (3) covariance prediction:
and (3) calculating an observation predicted value:
and (3) calculating innovation:
calculating innovation covariance:
and (3) calculating a likelihood function:
Λk＝N(zk；vk|k-1,Sk|k-1)
and (3) calculating gain:
whereinIs Sk|k-1The inverse of (1);
calculating the state:
and (3) calculating covariance:
the root mean square error of the interactive multi-model algorithm under 500 monte carlo simulations is compared with the 2 nd order interactive multi-model filtering method based on the mixed transfer distribution, as shown in fig. 1 and fig. 2.
The root mean square error of the high-order interactive multi-model filtering method based on the mixed transfer distribution under 500 Monte Carlo simulations is shown in FIG. 3 and FIG. 4.
By combining the hybrid transition distribution model with the generalized high-order interactive multi-model filtering method, the transition probability of the high-order model can be set easily, so that the high-order filtering algorithm can be flexibly applied without being influenced by the order.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.
Claims (9)
1. A high-order interactive multi-model filtering method based on mixed transfer distribution is characterized in that: the high-order interactive multi-model filtering method based on the mixed transfer distribution comprises the following steps:
the method comprises the following steps: obtaining n-order model sequence transition probability rho (m) by adopting a mixed transition distribution modelk|mk-n,...,mk-1)；
Step two: the estimated state vector isAnd a corresponding covariance ofProcessing the k moment in real time; when k is equal to 1, turning to step three; when k is 2, turning to step four; when k is more than or equal to 3 and less than or equal to n, turning to the sixth step; when k is>When n, turning to the seventh step;
step three: initializing the state when k is equal to 1, and then switching to the second step to process radar observation data at the moment when k is equal to k + 1;
step four: initializing the state when k is 2, and then turning to the fifth step;
step five: judging k, and when k is equal to n, determining the n-order model sequence probability U at the moment kk(mk-n+1,...,mk) N-order model sequence state estimationAnd withCorresponding covarianceAfter initialization, processing radar observation data at the moment when k is equal to k +1 in the second step; when k is not equal to n, directly executing step two to process radar observation data at the moment when k is equal to k + 1;
step six: after the interactive multi-model filtering algorithm is carried out on the state when k is more than or equal to 3 and less than or equal to n, the step is switched to the fifth step;
step seven: and after the generalized high-order interactive multi-model filtering is carried out on the state when k is larger than n, the second step is carried out to process radar observation data at the moment when k is equal to k + 1.
2. The method of claim 1, wherein the method comprises: in the first step, a mixed transition distribution model is adopted to obtain an n-order model sequence transition probability rho (m)k|mk-n,...,mk-1) The specific process comprises the following steps:
wherein m isjM is the model at time j, j is k-n, …, k, and the number of models is rjThe value range of (1) to r;is from the model mk-gTransfer to model mkThe probability of (a) of (b) being,is an element in a first order Markov chain, λgIs each step size coefficient, satisfying the following conditions:
3. the method of claim 2, wherein the method comprises: the model specifically comprises:
Xk+1＝Fk(mk)Xk+Gk(mk)uk(mk)+k(mk)vk(mk)
wherein XkIs determined by x-axis position x at time kkSpeed of x axisy-axis position ykSpeed of y axisA constituent state vector; fk(mk) Representing the model m at time kkSystem transfer matrix ofk(mk) Is an input control matrix, uk(mk) Is the input of a signal, and the signal is,k(mk) Is a matrix of noise coefficients, vk(mk) Is the k time model mkZero mean white Gaussian process noise with covariance of Qk(mk)；
Wherein T represents a sampling interval;
(1) when the model is a uniform motion model:
(2) when the model coordinates the turn model:
(3) when the model is a uniform acceleration motion model:
wherein, ax，ayAcceleration in the x-axis and y-axis directions, respectively.
4. The method of claim 3, wherein the method comprises: the specific process of initializing the state when k is 1 in the third step is as follows:
wherein z isk＝[xkyk]TIndicating radar received at time kObservation data, zk(j) Denotes zkThe jth value of (d); r isijIs the ith row and jth column element of the observed noise covariance R, i.e.
5. The method of claim 4, wherein the method comprises: the specific process of initializing the state when k is 2 in the fourth step is as follows:
initializing a k-time model probabilityState estimation of modelsCorresponding covariance
6. The method of claim 5, wherein the method comprises: in the fifth step, k is judged, and when k is equal to n, the state n-order model sequence probability U at the moment k is judgedk(mk-n+1,...,mk) N-order model sequence state estimationAnd withCorresponding covarianceThe specific process of initializing is as follows:
7. the method of claim 6, wherein the method comprises: the specific process of performing the interactive multi-model filtering algorithm on the state when k is more than or equal to 3 and less than or equal to n in the sixth step is as follows:
calculating the mixing probability:
where ρ (m)k|mk-1) Is a first order model transition probability, C1(mk) Is the normalization constant:
calculating a hybrid state estimate:
and (3) calculating the covariance corresponding to the mixed state estimation:
handleAndas input, Kalman filtering is performed to obtain state estimates of the models at time kCorresponding covarianceAnd likelihood function Λk(mk)；
Calculating the probability of the model at the moment k:
calculating the state at time k
ComputingCorresponding covariance
8. The method of claim 7, wherein the method comprises: the specific process of carrying out generalized high-order interactive multi-model filtering when k is greater than n in the step seven is as follows:
calculating the mixing probability:
wherein, Cn(mk-n+1,...,mk) Is a normalization constant;
calculating a mixed state estimation of the n-order model sequence:
computingThe corresponding covariance:
handleAndas input, Kalman filtering is carried out to obtain state estimation of each model sequence at the k momentCorresponding covarianceAnd likelihood function Λk(mk-n+1,...,mk)；
Calculating the n-order model sequence probability at the k moment:
calculating model probability at time k
Calculating the state at time k:
computingThe corresponding covariance:
9. the method of claim 8, wherein the method comprises: the Kalman filtering in the sixth step and the seventh step comprises the following specific steps:
and (3) state prediction:
whereinIs an input to the kalman filter;
and (3) covariance prediction:
whereinIs an input to the kalman filter;
and (3) calculating an observation predicted value:
wherein HkIs an observation matrix;
and (3) calculating innovation:
calculating innovation covariance:
r is the observed noise covariance,is HkTransposing;
and (3) calculating a likelihood function:
whereinDenotes zkObey mean value ofCovariance of Sk|k-1(ii) a gaussian distribution of;
and (3) calculating gain:
calculating the state:
and (3) calculating covariance:
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| CN108871365A (en) * | 2018-07-06 | 2018-11-23 | 哈尔滨工业大学 | Method for estimating state and system under a kind of constraint of course |
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